3.2 Problem Framework
3.2.3 Decision dependencies
As alluded to, although ISPs choose Internet technologies, their decisions, including
pricing, depend heavily on users and ICPs. For example, an ISP offering both IPv6
and (public) IPv4 connectivity might discount the IPv6 service, thereby attracting
users to that option and lowering the need for (expensive) public IPv4 addresses.
However, more IPv6 users also means higher translation costs, unless this entices
This creates a complex web of dependencies, whose impact is amplified by the
distributed decision process that prevails in the Internet. As we shall see, this can
make devising sound (profit maximizing) strategies difficult if not impossible. We
show in the next sections that these dependencies indeed play a critical role in IPv6
adoption, and by breaking only one of the links in the web of dependencies, the
outcomes change drastically.
3.2.4
Scenarios
In many technology adoption instances presence of multiple entrants, and lack of
consensus on a single choice among stakeholders can prevent a full market pene-
tration by any of those choices. While competition of alternative solutions can be
helpful in keeping the evolution of a technology on the right track, consensus on one
choice makes a full market penetration faster and easier. In the case of IPv6, a full
market penetration is required, if the Internet is to avoid permanent traffic trans-
lation, therefore, the Internet Engineering Task Force (IETF) standardized IPv6 as
the replacement for IPv4. However, due to the hurdles in front of IPv6 adoption,
other alternative solutions have become popular among some ISPs.
As different ISPs manage separate Autonomous Systems (ASes), their decisions
are to some extent independent of each other. This heterogeneity among ISPs can
lead them to offer (at least temporarily) different connectivity solutions. Since ISPs
nificant impact on IPv6 adoption compared to other Internet stakeholders. There-
fore and in order to investigate this impact, we consider two major scenarios: (i) a
scenario in which ISPs disagree on immediately offering IPv6 connectivity to their
users; and (ii) a scenario in which all ISPs offer IPv6 along with other connectivity
options to their users. Next, we describe these two scenarios in more details.
Disagreement on offering IPv6
In this scenario, one ISP is always assumed to offer IPv6, as otherwise the outcome
is trivial, i.e., stagnation in IPv6 adoption, while the other ISP offers either public
or private IPv4 addresses.
Given that the main competition IPv6 faces is the incumbent IPv4 Internet, we
consider the case of two ISPs, one having embraced IPv6 as the technology of choice
for its new customers24, while the other has decided to defer any migration and to
simply acquire additional public IPv4 addresses to accommodate new customers.
The first ISP needs to deploy address translation devices to allow its new (IPv6)
customers to connect to the legacy IPv4 Internet. This cost grows with the number
of users that choose IPv6, and decreases as more ICPs become IPv6 accessible25.
Conversely, while the second ISP does not incur translation costs, it needs to pur-
chase public IPv4 addresses for its new customers. Those costs are expected to rise
24T-Mobile has recently started to only assign IPv6 addresses to its Android 4.4 users (see [77]). 25Translation costs are assumed proportional to the volume of traffic that needs to be translated,
as public IPv4 addresses become scarcer.
Another variation of this scenario is when no ISP wants to incur the cost of
purchasing more public IPv4 addresses (or those addresses are unavailable for pur-
chase). ISPs that defer upgrading to IPv6 would then rely on private IPv4 addresses.
Offerings based on either IPv6 or private IPv4 addresses both require translation
(CGNs) to connect to the public IPv4 Internet. Translation costs for private IPv4
are likely to be lower than for IPv6, if only because of more mature technology
and/or greater operational familiarity and compatibility with the current Internet.
On the flip side, translation costs for private IPv4 keep increasing as more users
join, independent of how many ICPs become IPv6 accessible. We describe this
scenario in Appendix A.
Consensus on Offering IPv6
In this scenario, there exists a global consensus on offering IPv6 (along with other
service types), as a technology of choice to users, hence, all ISPs offer IPv6 and
another service, e.g., public IPv4.
On the technology choice front, this scenario is identical to the first one, namely,
both IPv6 and public IPv4 are available as connectivity options. The main difference
is that the two options are now systematically offered by all ISPs, and therefore
priced internally, as opposed to competitively, to maximize their own profit. The
services that ISPs offer (for free) along with their IPv6 services, but charge users
for those same services in IPv4, e.g., static addresses (http://www.vo.lu) etc. This
scenario is equivalent to having a monopolistic ISP that sets the price of both
connectivity choices.
3.3
Models
Based on the scenarios of the last section, we developed models that capture the
interactions and decision dependencies of ISPs, ICPs and users. As alluded to in
section 3.2.3, the decisions of users depends on the decisions of ICPs and ISPs, and
vice versa. ISPs are the selectors of the technology and affect the interactions of
the other two stakeholders through their decisions. This framework is common to
other environments, e.g., gaming platforms, where the number of game developers
and the number of gamers are affected by the decisions of the console provider.
Analyzing these frameworks is typically through a two-sided market setting [69].
The ISP is the market maker through its offering of connectivity options, while
users and ICPs are the two sides of the market that derive value from each other
through the ISP.
We assume that at each step, new and existing users evaluate the Internet
connectivity choices available to them through their local ISP(s)26 and select the 26According to http://www.broadbandmap.gov/summarize/nationwide, over 99% of the
one yielding to the highestutility. One obvious shortcoming of this model is the lack
of inertia in decision making of users, i.e., every user decides at each time epoch,
therefore, in section 3.6 we investigate the robustness of our results in scenarios
where the users face some form of inertia, e.g., contractual agreements. We define
a user’s utility in Section 3.3.1, but it depends primarily on the cost and quality of
her Internet connectivity.
Users are assumed heterogeneous, but primarily in their sensitivity to connec-
tivity quality27. We further assume (see [27] for a related discussion) that address
translation devices, if used, are the main contributors to degradation in connectivity
quality/functionality.
Because ICPs are part of the current Internet, they already have a public IPv4
address, and their only decision is whether or not to become IPv6 accessible. They
incur a cost when doing so (upgrading their existing IPv4 infrastructure and/or
update of operational processes), but unlike users that can revert their decisions, an
ICP’s decision to become IPv6 accessible is irreversible (once incurring the upgrade
cost). Next, we present the utility functions of the Internet stakeholders.
http://goo.gl/MjTPJ6).
27Coarser grain heterogeneity is also possible,e.g.,between, say, residential and enterprise users,
but adds significant complexity to the model. Similarly, heterogeneity in price sensitivity can also be included, but with again a cost in terms of complexity.
3.3.1
Users utility
Users derive aunit value from Internet connectivity, with price and quality affecting
their overall utility. An alternative model assumes heterogeneous values for different
connectivity options, however, since we use pricing as the control knob of the ISPs,
the former presentation is chosen (the outcomes are nevertheless similar). Recall
that quality is assumed to be primarily affected by (the presence of) translation
devices. A user’s utility is then captured through the following expression:
Uuser(σ) = 1−pR | {z }
VR
−σaRγR, (3.3.1)
whereRindexes connectivity options,pRis the price of typeRconnectivity (ppub. IPv4 >
pIPv6 > ppriv. IPv4) (alternatively VR is the value of option R), aR ∈ [0,1] quanti-
fies quality (translation) impairments for connectivity option R, if any (aR is 0 for
public IPv4 and positive for both private IPv4 and IPv6), γR is the fraction of the
Internet (ICPs) affected by those impairments, and σ denotes a user sensitivity to
quality impairments.
3.3.2
ICPs utility
ICPs derive revenues from users, and those revenues can be affected by connectivity
quality [73]. A major factor in an ICP’s decision to become IPv6 accessible28 is, 28As participation in events such “World IPv6 Launch Day” demonstrates, there are obviously
many other possible reasons for an ICP to become IPv6 accessible. However, even when those other motivations prevail, the importance of preserving connectivity quality remains,e.g.,through
therefore, the impact this decision can have on the revenue it generates from IPv6
users, and how this compares to the cost of upgrading to IPv6 (or convincing its
hosting provider to upgrade). Revenue improvements depend on the number of
IPv6 users and how they are affected by the ICP’s adoption of IPv6. In particular,
and as shown in [62], IPv6 and IPv4 connectivity quality are now mostly on par, so
that the main benefit of native IPv6 access is to eliminate the need for translation.
The cost of upgrading to IPv6 is largely a function of the “size” of the ICP’s
infrastructure. For simplicity, this size is assumed proportional to the Internet
user-base (the traffic volume an ICP sees grows with the Internet). The net util-
ity in(de)crease an ICP derives from becoming IPv6 accessible can, therefore, be
captured as follows:
∆6(ICP) = βn6a6−Sinfraθc6 (3.3.2)
where βn6 is the fraction of IPv6 users that an ICP can benefit from, a6 is the
per-user revenue gain from eliminating translation, and θc6 is the per-user upgrade
cost of the ICP’s infrastructure (of size Sinfra). β and θ capture heterogeneity in
revenue and cost, respectively, across ICPs.
3.3.3
ISP utility
An ISP’s utility (profit) depends on revenues derived from users29 and costs. Given
our aim of assessing the impact of offering different connectivity options, we focus
on their cost contributions and ignore other cost components. As costs differ across
connectivity options, we introduce the ISP’s utility function separately for each.
Public IPv4 only
An ISP that only offers public IPv4 connectivity has a utility function of the form:
Πpub. 4 =n4p4−C(n4−1)2+ (3.3.3)
n4is the number of users willing to payp4for public IPv4 connectivity, whileC(n4−
1)2+ =Cmax(0, n4−1)2 is the acquisition cost of the (n4−1) additional public IPv4
addresses the ISP needs beyond the “unit” block it already owns (to accommodate
its existing users). The quadratic function used for address acquisition costs seeks to
capture the growth in the price of public IPv4 addresses due to increasing scarcity.
Section 3.6 changes this assumption, and investigates the impact of other functions
on the models outcome.
29We ignore revenues from ICPs, as they are mostly independent from an ISP’s connectivity
IPv6 only (and IPv6↔IPv4 translation)
An ISP offering IPv6 connectivity has a utility of the form:
Π6 =n6p6−D6n6γ6, (3.3.4)
withn6 the number of users choosing IPv6 connectivity at a price ofp6,andD6n6γ6
the translation cost for those users. This expression assumes each user generates
1 unit of traffic distributed uniformly across ICPs, so that if γ6 ICPs are not IPv6
accessible, n6γ6 units of traffic must be translated at a unit cost of D6.
Public IPv4 and IPv6
An ISP offering both public IPv4 and IPv6 has a utility that is simply the sum of
Eqs. (3.3.3) and (3.3.4) and is of the form:
Π46 =n4p4−C(n4−1)+2 +n6p6−D6n6γ6. (3.3.5)
The next subsection explains the decision mechanism of the Internet stakehold-
ers, and the timing of those decisions.